DLMF:19.2.E16 (Q6112): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1ahdec

Revision as of 13:36, 2 January 2020

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DLMF:19.2.E16
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    Statements

    Defining formula
    el3 ⁡ ( x , k c , p ) = ∫ 0 arctan ⁡ x d θ ( cos 2 ⁡ θ + p ⁢ sin 2 ⁡ θ ) ⁢ cos 2 ⁡ θ + k c 2 ⁢ sin 2 ⁡ θ = Π ⁡ ( arctan ⁡ x , 1 - p , k ) , Bulirsch-integral-el-3 𝑥 subscript 𝑘 𝑐 𝑝 superscript subscript 0 𝑥 𝜃 2 𝜃 𝑝 2 𝜃 2 𝜃 superscript subscript 𝑘 𝑐 2 2 𝜃 elliptic-integral-third-kind-Pi 𝑥 1 𝑝 𝑘 {\displaystyle{\displaystyle\mathrm{el3}\left(x,k_{c},p\right)=\int_{0}^{% \operatorname{arctan}x}\frac{\mathrm{d}\theta}{({\cos^{2}}\theta+p{\sin^{2}}% \theta)\sqrt{{\cos^{2}}\theta+k_{c}^{2}{\sin^{2}}\theta}}=\Pi\left(% \operatorname{arctan}x,1-p,k\right),}}
    0 references
    DLMF id
    DLMF:19.2.E16
    0 references
    constraint
    x 2 ≠ - 1 / p superscript 𝑥 2 1 𝑝 {\displaystyle{\displaystyle x^{2}\neq-1/p}}
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
     
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